The stiffness mapping matrix for a planar compliant mechanism is analyzed using two different reference frames. The first is rigidly attached to the fixed body of the coupling, whilst the second is attached to the moving body of the coupling. It was found that, in general, these matrices are asymmetric when the coupling is loaded, and that one is the transpose of the other. This is an important result and can be considered an extension of the work done by Dimentberg, who derived a symmetrical stiffness mapping for an unloaded coupling. These new mappings are essential for the control of the coupling as it moves away from its unloaded position. Additionally, a third frame of reference which produces a symmetric mapping is examined and found to be identical to the Hessian matrix obtained from the second differentials of the elastic potential energy of the system. However, this symmetric mapping is not useful for control purposes and is only included to show that such a frame can be realized. Finally, static force loci for each of the reference frames are drawn to support the notion of frame-of-reference dependency.